7 problems

Three-component connectivity conjecture. The map $l_3$ is $(3n-\max\{2p_1+p_2+p_3,p_1+2p_2+p_3,p_1+p_2+2p_3\}-5)$-connected.

Taylor approximation connectivity conjecture. The map

Connectivity conjecture. The map $l_2$ is $(2n-\max\{2p+q,2q+p\}-3)$-connected.

Let $f:S^1\sqcup\dots\sqcup S^1\to\mathbb{R}^3$ be any map. Circle-map homotopic disjoinability conjecture. Every such map is homotopically disjoinable. Here homotopically disjoina…

Let $X_1\sqcup\dots\sqcup X_k$ be a disjoint union of fixed, not necessarily connected, components and let $f:X_1\sqcup\dots\sqcup X_k\to Q$ be a continuous map. A map is disjoinab…

Let $m$ be a positive integer and let $d>3$. Consider the space of link maps … A product of Milnor invariants of type $n$ gives, via configuration-space integrals, a generalized Mi…

Graph-complex surjectivity conjecture. The map from the whole graph complex induces a surjection in cohomology.